BOP – The Math

Using estimated bird density, average flight speed of migrating birds, and land area of Portland, we can estimate the quantity of Birds Over Portland during any one migration event.

The building blocks:

Dr. Sid Gauthreaux and Carroll Belser developed a calibration curve for interpreting radar reflectivity (measured in dBZ) in terms of birds km-3. (methodology can be read here)

Minimal migration: <5 dBZ — fewer than 59 birds per cubic kilometer
Light migration: 5-10 dBZ — approximating 59-71 birds per cubic kilometer
Moderate migration: 10-20 dBZ — approximating 71-227 birds per cubic kilometer
Heavy migration: 20-30 dBZ — approximating 227-1788 birds per cubic kilometer
Extreme: >30 dBZ — more than 1788 birds per cubic kilometer (very rare)

Birds vary in how fast they fly in migration.  Variables are species, topography, flight path  and wind/weather.  We’ll be conservative and use 20 mph or 30 kph. (Smithsonian fact sheet can be viewed here)

Portland has an estimated land mass of 375 sq km.

Just for the ease of calculation we’ll be conservative and say migrating birds occupy 1 kilometer of vertical airspace.  It’s actually more — see the Smithsonian fact sheet here.

So, now we can build this table:

dBZ 5                . 10               . 20               . 30                 . 30+
bpkm^3                   50                   65                 150                1,000                1,800
speed kph                   30                   30                   30                     30                     30
bph/km^2              1,500              1,950              4,500              30,000              54,000
bph/m^2              0.002              0.002              0.005                0.030                0.054
PDX 375 km^2                 375                 375                 375                   375                   375
Birds over Portland per hour          562,500          731,250       1,687,500        11,250,000        20,250,000
Hours of sustained flight 7          . 7         . 7       . 7         . 7            .
Birds over Portland per night       3,937,500       5,118,750     11,812,500        78,750,000      141,750,000


bpkm^3 = birds per cubic kilometer from Gauthreaux’s work

kph = bird’s average flight speed

bph/km^2 = birds per hour over head per square km of land mass

bph/m^2 = birds per hour per one square meter of land mass — directly over your head

That’s right!

During  light migration (5 dBZ) there are roughly a half a million birds per hour over Portland.  That’s around 4 million a night!

And during the heaviest (30 dBZ, which has been seen here — check the archives!) there are over 11 MILLION birds per hour over Portland.  I don’t believe this level could be sustained for the whole night flight but, if it could it would represent 140 million birds per night.

Typical readings are in the 10 to 20 dBZ range and that puts the number of birds at  roughly 750 thousand to 1.5 million birds per hour over Portland.  These levels are sustained regularly for the whole duration and that puts it at 5 to 10 million birds a night!

Who knows the actual counts.  These are just the numbers using conservative estimates based on best available data.  It’s really amazing.  So, if someone asks, “how many birds are over Portland?” the answer is LOTS!